It doesn't necessarily need to be sinking. It could have some sections flooded and not sink anymore... But yeah it's a bit of nitpick...specially if the boat it's stuck and cannot be moved by itself, which is the case here and while towing it it could eventually sink if some stuff continues to break or similar.

They're specifically refuting claims that it had been sunk. I don't see what your problem with that is.

The better wording might be 'British registered ship attacked by Houthi fighters, damaged and may sink' or something. It's very deliberately proving that the Houthi propaganda around its sinking is incorrect. That's not copium, it's news.